Fabian Furrer

Implementation of continuous-variable quantum key distribution with composable and one-sided-device-independent security against coherent attacks.

Tobias Gehring, 2 Vitus Händchen, Jörg Duhme, Fabian Furrer, Torsten Franz, 5 Christoph Pacher, Reinhard F. Werner, and Roman Schnabel 7, ∗ Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) and Institut für Gravitationsphysik, Leibniz Universität Hannover, Callinstraße 38, 30167 Hannover, Germany Department of Physics, Technical University of Denmark, Fysikvej, 2800 Kgs. Lyngby, Denmark Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannnover, Germany Department of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan, 113-0033 Institut für Fachdidaktik der Naturwissenschaften, Technische Universität Braunschweig, Bienroder Weg 82, 38106 Braunschweig, Germany Digital Safety & Security Department, AIT Austrian Institute of Technology GmbH, 1220 Vienna, Austria Institut für Laserphysik und Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, GermanySecret communication over public channels is one of the central pillars of a modern information society. Using quantum key distribution this is achieved without relying on the hardness of mathematical problems, which might be compromised by improved algorithms or by future quantum computers. State-of-the-art quantum key distribution requires composable security against coherent attacks for a finite number of distributed quantum states as well as robustness against implementation side channels. Here we present an implementation of continuous-variable quantum key distribution satisfying these requirements. Our implementation is based on the distribution of continuous-variable Einstein–Podolsky–Rosen entangled light. It is one-sided device independent, which means the security of the generated key is independent of any memoryfree attacks on the remote detector. Since continuous-variable encoding is compatible with conventional optical communication technology, our work is a step towards practical implementations of quantum key distribution with state-of-the-art security based solely on telecom components.

Position-momentum uncertainty relations in the presence of quantum memory

A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are thereby measured in terms of entropies providing a clear operational interpretation in information theory and cryptography. Recently, entropic uncertainty relations have been used to show that the uncertainty can be reduced in the presence of entanglement and to prove security of quantum cryptographic tasks. However, much of this recent progress has been focused on observables with only a finite number of outcomes not including Heisenberg’s original setting of position and momentum observables. Here, we show entropic uncertainty relations for general observables with discrete but infinite or continuous spectrum that take into account the power of an entangled observer. As an illustration, we evaluate the uncertainty relations for position and momentum measurements, which is operationally significant in that it implies security of a quantum key distribution scheme based on homodyne detection of squeezed Gaussian states.

Reverse Reconciliation Continuous Variable Quantum Key Distribution Based on the Uncertainty Principle

A big challenge in continuous variable quantum key distribution is to prove security against arbitrary coherent attacks including realistic assumptions such as finite-size effects. Recently, such a proof has been presented in [Phys. Rev. Lett. 109, 100502 (2012)] for a two-mode squeezed state protocol based on a novel uncertainty relation with quantum memories. But the transmission distances were fairly limited due to a direct reconciliation protocol. We prove here security against coherent attacks of a reverse reconciliation protocol under similar assumptions but allowing distances of over 16 km for experimentally feasible parameters. We further clarify the limitations when using the uncertainty relation with quantum memories in security proofs of continuous variable quantum key distribution.

The smooth entropy formalism for von Neumann algebras

We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

State-dependent approach to entropic measurement–disturbance relations

Abstract Heisenbergs intuition was that there should be a trade-off between measuring a particles position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two complementary observables can be jointly measured. Here, we provide an alternative approach based on how enhancing the predictability of one observable necessarily disturbs a complementary one. Our measurement–disturbance relation refers to a clear operational scenario and is expressed by entropic quantities with clear statistical meaning. We show that our relation is perfectly tight for all measurement strengths in an existing experimental setup involving qubit measurements.

Optimality of entropic uncertainty relations

The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be non-optimal. Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of the corresponding uncertainties. In this work we establish optimal uncertainty relations by characterising the optimal lower bound in scenarios similar to the Maassen-Uffink type. We disprove a conjecture by Englert et al. and generalise various previous results. However, we are still far from a complete understanding and, based on numerical investigation and analytical results in small dimension, we present a number of conjectures.

Information-theoretical analysis of topological entanglement entropy and multipartite correlations

A special feature of the ground state in a topologically ordered phase is the existence of large scale correlations depending only on the topology of the regions. These correlations can be detected by the topological entanglement entropy or by a measure called irreducible correlation. We show that these two measures coincide for states obeying an area law and having zero-correlation length. Moreover, we provide an operational meaning for these measures by proving its equivalence to the optimal rate of a particular class of secret sharing protocols. This establishes an information-theoretical approach to multipartite correlations in topologically ordered systems.

Extremal quantum correlations and cryptographic security.

We investigate a fundamental property of device-independent security in quantum cryptography by characterizing probability distributions which are necessarily independent of the measurement results of any eavesdropper. We show that probability distributions that are secure in this sense are exactly the extremal quantum probability distributions. This allows us to give a characterization of security in algebraic terms. We apply the method to common examples for two-party as well as multiparty setups and present a scheme for verifying security of probability distributions with two parties, two measurement settings, and two outcomes.

Operational Meaning of Entanglement Entropy in Anyonic Systems

Anyons are modeled by topologically protected Hilbert spaces which obey complex superselection rules restricting possible operations. As a result, entanglement associated with anyonic degrees of freedom follows distinguished principles. In particular, a decomposition of local subsystems into tensor factors is impossible, whereas the tensor product structure is a foundation of conventional entanglement theory. We formulate bipartite entanglement theory for pure anyonic states and analyze its properties as a non-local resource for quantum information processing. We introduce a new entanglement measure, asymptotic entanglement entropy (AEE), and show that it characterizes distillable entanglement and entanglement cost similarly to entanglement entropy in conventional systems. AEE depends not only on the Schmidt coefficients but also on the quantum dimensions of the anyons shared by the local subsystems. Moreover, it turns out that the AEE coincides with the entanglement gain by anyonic excitations in certain topologically ordered phases.

Repeaters for continuous-variable quantum communication

Optical telecommunication is at the heart of todays internet and is currently enabled by the transmission of intense optical signals between remote locations. As we look to the future of telecommunication, quantum mechanics promise new ways to be able to transmit and process that information. Demonstrations of quantum key distribution and quantum teleportation using multiphoton states have been performed, but only over ranges limited to a few hundred kilometers. To go beyond this, we need repeaters that are compatible with these quantum multiphoton continuous-variable pulses. Here we present a design for continuous-variable quantum repeaters that can distribute entangled and pure two-mode squeezed states over arbitrarily long distances with a success probability that scales only polynomially with distance. The proposed quantum repeater is composed from several basic known building blocks such as non-Gaussian operations for entanglement distillation and an iterative Gaussification protocol (for retaining the Gaussian character of the final state), but complemented with a heralded non-Gaussian entanglement swapping protocol, which allows us to avoid extensive iterations of quantum Gaussification. We characterize the performance of this scheme in terms of key rates for quantum key distribution and show a secure key can be generated over thousands of kilometers.